Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder

TL;DR

This study investigates how the size of the computational domain affects direct numerical simulations of Taylor-Couette turbulence, revealing that domain dimensions influence flow structures, velocity profiles, and spectra, with smaller domains still capturing key features.

Contribution

It systematically analyzes the impact of domain size on simulation accuracy and flow characteristics in Taylor-Couette turbulence, highlighting the importance of axial and azimuthal extents.

Findings

Smallest box reproduces torque and mean velocity profiles accurately.

Axial extent influences Taylor-rolls and correlation spectra.

Larger azimuthal extent allows development of azimuthal wave patterns.

Abstract

In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain ("box") size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes, with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to $\eta=r_i/r_o=0.909$, and the outer was kept stationary, while the inner rotated at a Reynolds number $Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is also found to play a significant role, as larger boxes allow for azimuthal wave-like patterns in the Taylor rolls to develop, which affects the statistics in the bulk region. For all boxes studied, the spectra does not reach a box independent maximum.